Question

Page 114 question 5 Select the 2 missing x values from the table to complete itSelect all that apply (2 answers)Complete the following table for h(x)=-(1/4)^xA 0B 2C-2D 3E -3F 1G -1

Answer 1

We are given the function:

$y=-\mleft(\frac{1}{4}\mright)^x$

And the table contains two values of y (-16 and -64) for whose we need to find the corresponding values of x.

For y = -64:

$\begin{gathered} -\mleft(\frac{1}{4}\mright)^x=-64 \\ \text{Multiply by -1:} \\ \mleft(\frac{1}{4}\mright)^x=64 \end{gathered}$

Applying properties of the exponents:

$4^{-x}=4^3$

Get rid of the bases, we equate the exponents:

x = -3

For y = -16:

$\begin{gathered} -\mleft(\frac{1}{4}\mright)^x=-16 \\ \text{Multiply by -1:} \\ \mleft(\frac{1}{4}\mright)^x=16 \end{gathered}$

Applying properties of the exponents:

$4^{-x}=4^2$

Equating the exponents:

x = -2

The values of the table are:

-2 , 16

-3 , 64